This was a common problem from what I remember when I was a tech at Saturn. Most likely a valve body is needed. If I remember correctly there was a bulletin to replace the upper half of the valve body because the shaft would either become hung up or solenoid failure. the solenoid usually gave a code. Since you're just having the reverse issue I would recommend upper valve body and transfer the solenoids over. This was fairly easy repair and took 30 mins. Two cautions to remember.. first is there are a few steel balls which i recommend using jelly to hold in place (I think there is 3)when reinstalling and don't take all the 8mm bolts out which will seperate the vale body halves while attacted to the trans. Would not want the balls to fall into the trans, so disassemble on a flat surface (bench). Second is remember to attach the shaft from the valve body to the rod. Hopefully this helps.

The most common cause of delay or no reverse, other than the valve body, is a loose main-shaft nut. The symptoms will most likely occur when the vehicle is hot, and may also exhibit a soft or flared 2nd gear up-shift. A loose main-shaft nut can cause a Leak in the 2nd clutch circuit. When the nut is loose, the main-shaft walks back and forth In the middle of the case. This causes a small gap between the 1st clutch and the nut, which is where the leak in the 2nd clutch circuit appears. A new main-shaft nut should be replaced with every repair, since it has a factory thread locker. The nut can be accessed by removing the side cover, which means the unit does not have to be removed to replace it. The nut, and this is very important, should be torqued to 111 ft. lbs. The Saturn part number for the main-shaft nut is 21001680.

Another common no reverse condition is a faulty or defective vehicle speed sensor. The input from the VSS to the PCM should always read less than 5 mph. This allows the PCM to command high line pressure, which in turn will move the servo apply valve (1992-up models only) to an open position, thus opening up the passage to allow oil to the forward/reverse servo piston. If the VSS is defective (thus reading 5 mph or above on your scan tool), the PCM will command low line pressure, thus not feeding oil to the forward/reverse servo piston. In turn, the slider assembly will not move, causing a no reverse condition.

Another problem that occurs, especially when the unit has been removed, is an incorrectly adjusted pattern select switch, which we all commonly know as the manual lever positioning switch. If the pattern select switch is not adjusted properly, a no reverse condition, as well as loss of drive and/or erratic or harsh shifting can occur. To adjust the pattern select switch, put the selector in the D4 position. DO NOT start the vehicle. Connect an ohm meter to the switch. Rotate the switch until the ohm meter reads continuity. Once a reading is obtained, tighten the pattern select switch. Once again, the valve body is still the main cause for reverse as well as forward issues with the TAAT. But as you can see, there can be other areas that may also need to be addressed.

i bought a 96 sw2 with 120k on her... the car has always delayed going into reverse and had slight shifting issues between 2nd and 3rd. I changed the tranny fluid and filter a few months back which made shifts smoother, but it still has the same issues. The point is, a year and a half later I have 170k and the problem has not changed for better or worse. I always make sure my foot stays on the brake until I feel the car shift into reverse and ALWAYS use my e-brake...just a couple of tips that I think have helped keep her running...good luck.